(168$/,4,905*65640*9(168$/,4,905*65640*9
&63;4, 8:0*3,
#7805.
5+05.(55:,85,:;*:0659,(>97786(*/ 7:04(35+05.(55:,85,:;*:0659,(>97786(*/ 7:04(3
5+8,=,/8,59
%50<,890:>6-68:/,856=(
6336=:/09(5+(++0:065(3=6829(:/::799*/63(8=6829;50,+;4:0,
!(8:6-:/,*65640*9644659
,:;9256=/6=(**,99:6:/09+6*;4,5:),5,A:9>6;
67>80./:@)>(168$/,4,905*65640*9
",*644,5+,+0:(:065",*644,5+,+0:(:065
,/8,595+8,=5+05.(55:,85,:;*:0659,(>97786(*/ 7:04(3
(168$/,4,905
*65640*9
<(03()3,(:/::799*/63(8=6829;50,+;4:0,<63099
$/098:0*3,09)86;./::6>6;-68-8,,(5+67,5(**,99)>:/,6;85(39(:%#*/63(8'6829:/(9),,5
(**,7:,+-6805*3;906505(168$/,4,905*65640*9)>(5(;:/680?,+,+0:686-%#*/63(8'682968468,
05-684(:06573,(9,*65:(*:9*/63(8=6829;50,+;
--,590<,(:,80(39#:(:,4,5:(:,80(3936*(:,+05%#*/63(8'6829*64,-864()86(+8(5.,6-96;8*,9(5+
:04,7,806+9#64,6-:/,9,4(:,80(394(>*65:(056--,590<,9:,8,6:>7,90+,(9<09;(39683(5.;(.,
37
Ending an Internet Auction:
Is eBay’s Approach Optimal?
Andrew Behrens
ABSTRACT. Internet auctions can be ended in different ways. EBay auctions, for example,
end at a predetermined time while Amazon auctions do not. The auctions at Amazon are
extended by ten minutes if a bid is submitted within the last ten minutes of an auction.
EBay’s hard closing rule induces bidding strategies that can produce inefficient results.
Nevertheless, a hard close ending rule is more efficient than the automatic extension rule
used by Amazon. EBay’s hard closing rule can be modified to resemble a Vickrey second-
price auction. The modifications would make auctions on eBay more efficient.
I. Introduction
Going once, going twice, sold. The phrase is synonymous with the word
auction. The phrase describes the auction-ending procedure with which
most people are familiar. The proliferation of internet auctions is
changing the way auctions are ended. The primary advantage of internet
auctions is that they have lower transaction costs than traditional auctions.
From the bidder’s perspective the amount of time and effort spent bidding
is a major component of the transaction costs of an auction. The time
spent bidding is heavily influenced by the way an auction is ended.
Klemperer [2002, 19] said that “the most important features of an auction
are its robustness against collusion and its attractiveness to potential
bidders”. Which ending rule performs best under these criteria?
EBay auctions end at a set time, a rule which is called a hard close.
An auction’s ending rule affects the auction’s attractiveness to bidders
through the transaction cost of bidding. The transaction cost of bidding
increases in importance as the sale price of the good decreases. Items
auctioned on eBay do not usually have a high value, so transactions cost
matter.
Collusion and cheating will also be shown to be dependant upon the
auction’s ending rule. A hard close has lower transaction costs of
bidding, and is more robust against collusion than an auction that does not
have a set ending time. Altering eBay’s hard close to resemble a Vickrey
auction would improve the auction’s robustness against collusion. The
change would decrease the transaction cost of bidding, which would
Major Themes in Economics, Spring 2004
38
attract more bidders.
II. The Auction Structure on eBay
The bidding process on eBay is straightforward. The bidder who submits
the highest bid before the auction ends wins. The auction appears to be
a traditional English ascending price auction, and many naïve bidders act
as though it is. In an English auction bidders sequentially outbid one
another until only one bidder is willing to bid higher than anyone else.
EBay auctions end when time runs out. Bidders cannot continually raise
their bids like they could in an English auction. The “hard” closing time
has given rise to a practice known on eBay as “sniping”. Sniping occurs
when a bidder submits a bid with only minutes or seconds remaining in
the auction. The sniper attempts to successfully submit a bid such that
another bidder does not have sufficient time to respond with a higher bid.
Sniping is likened to a Vickrey auction. In 1961 William Vickrey
analyzed the revenue generated from different auction formats. The
formats were the English auction, the Dutch descending auction, the first-
price sealed bid auction, and the second-price sealed bid auction. Vickrey
showed that the four formats are revenue equivalent under some
circumstances [1961, 20]. Auction theorists incorrectly recognized
Vickrey as the creator of the second-price sealed bid format [Lucking-
Reiley, 2000, 3]. The second-price sealed bid format is known as the
Vickrey auction. In a Vickrey auction bidders submit one value to the
auctioneer. When time expires the item is awarded to the bidder with the
highest bid. The price the winner pays is equal to the second highest bid.
A sniper pays one increment above the highest submitted bid, but less
than he is willing to pay.
Roth and Ockenfels [2002, 2] show that Amazon auctions deter
sniping by ensuring that the last ten minutes of an auction are free of
bidding. Sniping is deterred by extending the closing time of an auction
by ten minutes whenever a bid is placed during the last ten minutes of an
auction. Amazon auctions are pure English auctions. EBay has
implemented a proxy bidding system to combat sniping. The proxy
resembles a Vickrey auction. A bidder inputs a maximum valuation and
the proxy will outbid any other bid lower than the maximum. If the proxy
bidder wins, the price will be one increment above the next highest bid.
Unlike a Vickrey auction the maximum valuation is not sealed. The
Behrens: Ending an Internet Auction
39
bidder always has the option to raise the valuation, and can lower it to the
level of the last submitted bid. Potential inefficiencies are created by the
coexistence of a hard closing time and a non-sealed bidding format. The
hard close guarantees the opportunity to snipe. The most efficient
outcome of sniping resembles a Vickrey auction. The efficiency of an
eBay auction will be equal to or less than the efficiency obtainable by
using a pure Vickrey auction format.
III. Cheating
A discussion of the fear and effect of cheating is necessary when
analyzing bidding behavior. Cheating can take two forms. In the first
form the seller gains an unfair advantage against the bidders. In the
second form the bidders collude against the seller. Cheating or the fear
of cheating is one of the two reasons why Vickrey auctions are not more
common [Rothkopf, 1990, 14]. The second reason is that bidders do not
want to disclose their valuation when it can be used against them in future
auctions. When there are post-auction negotiations a seller gains from
knowing the true valuation of the buyer. The true valuation of a bidder
is valuable information in markets for goods that are identical and
frequently auctioned. A seller must cheat to take full advantage of the
bidder’s true valuation.
Collusion against the seller in an Internet auction is rare because it is
unlikely that all potential buyers can meet before an auction begins. Roth
and Ockenfels [2002, 3] describe an equilibrium in which bidders collude
against an eBay seller using snipe bids. Collusion occurs without
communication prior to the auction. Bidders with high valuations decide
to snipe bid. The expected benefit of winning the auction at a low price
outweighs the probability of not submitting a winning bid. The bidders
are implicitly colluding against the seller to keep the price of the item
low. Collusion against the seller is more likely to occur when valuations
are interdependent, but may also occur when valuations are strictly
private.
Sellers have a greater opportunity to cheat in Vickrey auctions. The
dominant strategy of a bidder in a Vickrey auction is to bid his highest
valuation because he will only pay an increment above the second highest
bid. When seller and facilitator are one entity it is easy to inflate the
second highest bid or solicit a higher losing bid from a friendly third
party. Even if the seller is not running the auction the facilitator may
Major Themes in Economics, Spring 2004
40
have an incentive to inflate the price of the item. Portions of a
facilitator’s commissions are usually based on the final sale price. Some
sellers may have the power to pressure the facilitator to inflate the second
highest price. Lucking-Reiley’s [2000, 7] paper, “Vickrey Auctions in
Practice” contains the confession of a stamp auctioneer who left the
business because the temptation to artificially raise the second highest bid
was too great for him. EBay as a facilitator has a small stake in the
selling price of an item. Most of the fees eBay collects are independent
of the final sale price. It is assumed that eBay is rational and does not
have enough incentives to artificially raise sale prices.
Shill bidding is the most common form of seller cheating. A shill bid
occurs when the seller bids on her own item or employs someone to do so.
The purpose of the shill bid is to raise the second highest price. If the
bidder with the highest valuation were incrementally bidding he would
have to raise his bid to beat the shill bid. If the bidder is using the proxy
bidding system, the proxy will automatically raise the bid. In either
instance the shill bid creates artificial competition for the item. If the
shill bid is higher than the highest valuation of the true bidders then the
seller buys her own item. The seller must pay the transaction costs again
to sell the item. High transaction costs discourage the practice of shill
bidding. EBay initially encouraged sellers to bid in their own auctions if
they did not like the highest bid [eBay, 2004, para. 12]. They have since
realized the implications of shill bidding, and have banned it. EBay relies
on the diligence of its bidders to report shill bidding. Bidders discover
shill bidding by analyzing the bid history of a seller’s auctions. First time
violators are suspended. A second violation will result in a lifetime ban.
Detection of shill bidding is difficult when items are of low value or the
sellers rarely perform shill bidding. The U.S Department of Justice has
successfully prosecuted a few high profile cases of shill bidding. One of
the more infamous examples involved the auction of a fake Richard
Diebenkorn painting that sold for just over $135,000 [United States
Department of Justice 2001, 2].
Buyers have their own defense against shill bidding. Shill bidders
need to know that an individual values the item being auctioned. If a
bidder bids early or enters a proxy bid the seller will see that the bidder
values the item. As others bid against the early bidder, the early bidder
or his proxy will react with a higher bid. Shill bidding will occur when
only the early bidder remains. The shill bidder will provide artificial
competition for the early bidder until the price has reached an acceptable
Behrens: Ending an Internet Auction
41
level. The early bidder is better off if he hides his valuation. By snipe
bidding in the closing seconds the seller will not have time to enter a shill
bid. A seller could shill bid before the snipe bid is placed. If all bidders
are snipers, then the shill bidder can place only one bid. Submitting one
shill bid is equivalent to legally setting a reserve price. The shill bidder
needs a legitimate incremental bidder or a second shill bidder to bid
against. As shill bidding becomes more pervasive more bidders will
become snipe bidders. Actual shill bidding does not even need to occur
to induce bidders to snipe. The fear of shill bidding alone makes sniping
a rational bidding strategy.
IV. Market Depth
As auction participation increases, ceteris paribus, auction efficiency
increases [Swinkels, 1999, 17]. The competition added by new bidders
increases the revenue generated by an auction. For example, a sniper will
enter a bid of a magnitude related to the number of bidders he believes
will enter a snipe bid. If he expects many competing snipe bids he will
bid slightly higher. Any auction structure will be inefficient if the number
of bidders does not create a sufficient level of competition.
What aspects of eBay’s auctions attract bidders to the market? Lower
transaction costs attract entrants. It will be shown that the hard closing
rule and proxy bidding option lower the cost of bidding on eBay. Some
bidders that snipe say that it provides a kind of thrill or excitement that is
missing in other auctions [Steiner, 2002, para. 5]. The thrill could attract
risk-seeking bidders that normal auctions do not. Roth and Ockenfels
[2002, 4] showed that many more antique auctions take place on eBay
than on Amazon. Antique buyers prefer to use eBay’s auction structure
because it is more likely to afford them a higher profit. As of December
31, 2003 eBay had over 28 million users who had been active in the
previous twelve months [eBay, 2002b, para. 10]. The auction structure
of eBay is attractive to bidders.
A. INTERDEPENDENT VALUATION
The most transparent breakdown of the Vickrey Auction format is when
valuations are interdependent [Perry, 2002, 1]. Interdependent valuation
occurs when any individual’s valuation is affected by the bids of others.
Common valuations are a special case of interdependent valuations.
Major Themes in Economics, Spring 2004
42
Common values occur when each buyer’s valuation is so extremely
dependent upon the valuation of others that all buyers will have equal
valuations. In a Vickrey auction the maximum valuation of each bidder
is sealed. Bidders are unable to learn from the bids of others. Perry
[2002, 10] suggests that an auction with multiple rounds can assure that
bidders reveal valuations before the final bids are made. Multiple round
auctions hinge on the bidder’s incentives to reveal their valuations in the
early rounds. Crèmer [1985, 11] and Dasgupta [2000, 25] suggest that
bidders submit a valuation distribution that is conditional on other
bidders’ valuations. In reality the bidders themselves may not know how
they will react to the bids of others.
The valuation of antiques is usually interdependent. One type of
interdependent valuation occurs when some bidders are known to have
knowledge that other bidders do not. The insider has more information
about the true value of the antique. A bidder who is not an insider is
called a naïve bidder. The bidding behavior of identified insiders
provides information to other bidders. When an insider continues to bid,
naïve bidders learn of the insider’s higher valuation. The naïve bidders
will then raise their valuation to match the signal they receive from the
insider’s bid. When an insider ceases to bid, other bidders learn that the
current bid is greater than or equal to the insider’s valuation. Naïve
bidders will then lower their valuation so as not to pay more for the
antique than it is truly worth to them. The amount by which each naïve
bidder’s valuation changes is unique, but is directly related to the bidding
behavior of the insider.
A second instance of interdependent valuation in antique auctions is
associated with the theory of a Veblen Good. A Veblen Good’s high
price increases the status of its owner. A collector in search of a Veblen
Good obtains utility from winning an auction over bidders who were
capable of paying a high price for the antique. The presence of high bids
for an item may increase the value of the item in the minds of collectors
who desire Veblen Goods. A collector who seeks a Veblen Good will
value an item higher if it has received high bids.
Surely there is value in knowing the bids of others. A standard
Vickrey auction is inefficient because it is impossible to obtain
information about other bidders’ valuations. A buyer who realizes there
is value in his bid will snipe bid on eBay to protect the value of his
information. The insider’s true valuation is never revealed because he
only bids enough to beat the current price. If the insider wins, the price
Behrens: Ending an Internet Auction
43
paid will be equal to an increment above the second highest bid. All
buyers with valuable information will rationally bid in this manner. Due
to the lack of information all bidders will be uncertain about their
valuations. Insiders will attempt to submit a last second bid based upon
their imperfect knowledge of other insiders’ valuations.
EBay’s proxy bidding system cannot overcome inefficiency caused
by interdependent valuations. The proxy does not allow a buyer to enter
a maximum valuation that is dependent upon the bids of others.
Experienced bidders will submit bids late on eBay and will submit bids
early on Amazon [Roth, 2002, 7]. The difference could be due to a self-
selection of buyers and sellers to different auctions. Roth and Ockenfels
conclude that:
The clear difference observed in the amount of late bidding on
eBay and Amazon is strong evidence that, as predicted both at
equilibrium and when some bidders are unsophisticated, the hard
close gives bidders an incentive to bid late, in both private- and
common-value auctions. This evidence is strengthened by the
observations that (i) the difference is even clearer among more
experienced bidders, and (ii) there is more late bidding for eBay
Antiques than for eBay Computers [2002, 9].
The assumption is that antiques are more unique than computers. The
value of the antique is more uncertain. The uncertainty makes the
information of the insiders, or experienced bidders, more valuable.
Bidders perform sniping in order to protect the value of their information.
Sniping transforms the auction into a Vickrey auction with interdependent
values. A Vickrey auction will generate less revenue than an English
auction under interdependent values [Lucking-Reiley, 1999, 3]. Buyers
bid in a manner that reflects a Vickrey auction rather than bidding
incrementally because it minimizes the price they may pay for the item.
B. TRANSACTION COSTS
The main advantage of Internet auctions and the Internet in general is that
it reduces transaction costs. Traditional auctions like those held at
Sotheby’s require a bidder to be present at the auction. Bidders incur the
implicit and explicit costs of travel. Of course an agent can be hired to
bid in place of the buyer. The agent will collect a fee for his services and
Major Themes in Economics, Spring 2004
44
may or may not be as effective as the buyer would have been. William
Vickrey’s second price sealed auction does not require buyers to meet for
the auction. The bid merely consists of a maximum value that is mailed,
phoned, faxed, or otherwise communicated to the auctioneer anytime
before the auction closes. A Vickrey auction has a lower transaction cost
of bidding than an English auction.
Like typical auctions, Internet auctions have different transaction
costs of bidding. Internet auctions do not require bidders to gather in a
single room. Different auction formats require the buyer to spend more
or less time bidding. EBay, in its best form, requires as much effort as
any sealed bid auction. The least cost way to submit a bid on eBay is to
utilize the proxy bidding system. Submitting a proxy bid may not be the
best strategy to win the item at a low cost. If the strategy of the bidder is
to snipe, then the bidder must be signed onto eBay at the close of the
auction. Companies have formed that specialize in sniping for their
customers. Sniping has a slightly higher transaction cost of bidding than
a Vickrey auction or proxy bid.
Amazon’s ending rule creates higher transaction costs of bidding than
eBay. Bidders must be signed onto Amazon for the last scheduled ten
minutes of the auction. The bidder must stay at the auction site until the
going, going, gone period is over. The auctioning of the “Bartman Ball”
or “Infamous Cubs Ball” is a recent example. The ending rule of the
auction was identical to Amazon. MastroNet Inc. [2003, 1], the
auctioneer and owner of the ball, scheduled the auction to end at 10:00
P.M. on Thursday December 18, 2003. At 3:00 A.M. the next morning,
ten minutes passed without a new bid and the auction ended. The ball
was sold for over $106,000. This extreme example is only likely to occur
in instances where the auction item has an exceptionally high value.
A sealed bid auction has the lowest transaction cost of bidding. EBay
has a slightly higher transaction cost of bidding because sniping can be
a dominant strategy. Amazon’s transaction cost of bidding is vaguely
higher than eBay’s. Transaction costs of bidding are usually small, but
they can be significant when the value of the auctioned good is also small.
The differences in transaction costs of bidding among auction formats are
usually overshadowed by other factors, such as the cost or benefit of
collusion.
V. The Future of Sniping on eBay
There are three plausible, mutually exclusive ways that eBay can handle
Behrens: Ending an Internet Auction
45
sniping in the future. Option one is that eBay will do nothing. Bidders
will continue to snipe on their own, through third party servers, or with
third party software. No change is optimal if eBay feels that the hard
close rule attracts buyers and has positive net effect on auction revenue.
EBay has been profitable under the “hard” close structure, and is
unconcerned with the efficient allocation of the auctioned goods. Making
major changes to a business that is profitable is an option that is rarely
chosen by a public corporation. The two other alternatives require eBay
to adopt rules that will make their auctions resemble either a pure English
ascending auction or a pure second-price Vickrey auction.
Automatically extending the closing time of an auction when a snipe
bid is placed has been shown to curtail sniping [Roth, 2002, 2].
Automatic extension is a change commonly suggested by opponents of
sniping. The resulting auction would be nearly identical to Amazon’s
auction structure. A replication of Amazon’s structure is not likely for a
couple of reasons. First, eBay has been much more successful with
auctions than Amazon. EBay will not emulate a weak competitor without
legal or financial pressure. Second, English auctions strictly favor the
bidder with the highest valuation. The low value bidder has little
incentive to bid in an auction he cannot win. Predatory bidding by high
value bidders against lower value bidders may push competition below an
efficient level. Third, English auctions have high transaction costs of
bidding because of the uncertain length of the auction.
If change is to take place, eBay will likely adopt a bidding structure
that resembles a Vickrey auction. Vickrey auctions have low transaction
costs of bidding. Bidders only need to commit time to privately valuing
the item and placing a bid. Vickrey auctions on eBay would not inspire
the fear of cheating that occurs in other Vickrey auctions. Bidders are
likely to believe that eBay will not collude with sellers to shill bid. EBay
can strengthen the confidence of bidders by lowering the revenue that is
based on the final sale price. It is more difficult for a seller to shill bid in
a Vickrey auction because they do not have information on bidders’
valuations until after the auction.
Auction theory is supportive of Vickrey auctions, but theory is not the
main reason why eBay would change to a Vickrey format. Companies
sell software and services that will place a snipe bid for the bidder. Some
software is free but most of the companies are compensated for their
services and software. A survey of the sniping industry by
AuctionBytes.com [2003] shows that in 2002 these companies had at least
Major Themes in Economics, Spring 2004
46
410,000 customers that placed at least 351,000 bids per week. The
numbers do not include snipers who use software or services that did not
report figures. None of the sniping companies can guarantee that a snipe
bid will even be submitted. Assuming that each of the snipe bids cost an
industry low of $0.25 per bid, 351,000 snipe bids per week will generate
annual revenue of $4.5 million [AuctionBytes.com, 2003]. The heads of
two sniping services companies claimed that 5% of all auctions on eBay
in 2002 involved sniping [Glasner, 2002, 18]. There were 638 million
auctions on eBay in 2002 [eBay, 2002a, 1]. Assuming only one snipe bid
occurred in each of the sniped auctions, there would have been 32 million
snipe bids in 2002. At $0.25 per snipe bid, annual revenue would have
been $8 million. The revenues are small compared to eBay’s total
revenue, but it is still a significant amount of money. In 2002 the
additional revenue would have increased earnings per share of eBay’s
stock by 2 to 3.5 cents and would likely have a high net margin [eBay,
2002c].
EBay can easily capture sniping revenue. If eBay were to provide its
own sniping software it would eliminate all competition because it will
be directly connected with the auction. Snipe bids placed through an
eBay sniping service would always be submitted successfully. EBay
could couple its proxy-bidding agent to the sniping service so that a
winning bidder will only pay the second highest bid. If this change
occurred valuations would be submitted based solely upon the valuation
of each bidder. The valuations would not be revealed until the auction is
over, and the bidder would pay the second highest price. The auction
would be a pure Vickrey auction.
VI. Conclusion
A hard closing rule is optimal in Internet auctions of low value items in
order to keep transaction costs low. Low transaction costs of bidding
enable more bidders to participate, which increases competition,
efficiency, and revenue. Sniping is a rational response to a hard closing
time and fear of collusion. The structure of eBay auctions is not likely to
change. If change does occur it will likely be a move towards a pure
Vickrey auction because it will allow eBay to capture rents that sniping
agents have been earning. The “hard” close auction and pure Vickrey
auctions are inefficient formats for auctioning items that have strong
interdependent values.
Behrens: Ending an Internet Auction
47
Auctions of similar goods are commonly held concurrently or
sequentially. Timing can alter the conclusions of some research that has
been utilized in this paper. The effects of timing would be a useful
extension of this paper.
References
AuctionBytes.com (2003), “Sniping Services at a Glance,”
http://www.auctionbytes.com/cab/pages/sniping
Crèmer, J., McLean, R.P. (1985), “Optimal Selling Strategies Under Uncertainty for a
Discriminating Monopolist When Demands are Interdependent” Econometrica,
53:345-362.
Dasgupta, P., Maskin, E. (2000), “Efficient Auctions,” Quarterly Journal of Economics,
115:341-388.
EBay (2002a), “2002 Annual Report: Letter to Shareholders,”
http://www.ebay.com/2002annualreport/shareholderletter.html
EBay (2002b), “United States Securities and Exchange Commission Form
10-K: Item 1,”
http://www.shareholder.com/common/edgar/1065088/891618-03-1538/03-
00.html#F88540E10VK_HTM_001
EBay (2002c), “United States Securities and Exchange Commission Form
10-K: Consolidated Statement of Income,”
http://www.shareholder.com/common/edgar/1065088/891618-03-1538/03-
00.html#F88540E10VK_HTM_022
EBay (2004), “Shill Bidding: What It Is and Why It’s Not Permitted on eBay,”
http://pages.ebay.com/help/community/shillBidding.html
Glasner, Joanna (2002), “EBay Bidders Sold on Sniping,” Wired News,
http://www.wired.com/news/business/o,1367,55204,00.html
Klemperer, Paul (2002), “What Really Matters in Auction Design,” Journal of Economic
Perspectives, 16:169-189.
Lucking-Reiley, David (1999), “Using Field Experiments to Test Equivalence Between
Auction Formats: Magic on the Internet,” The American Economic Review, 89:1063-
1081.
Lucking-Reiley, David (2000), “Vickrey Auctions in Practice: From Nineteenth-Century
Philately to Twenty-First-Century E-Commerce,” Journal of Economic Perspectives,
14:183-192.
MastroNet Inc. (2003), “Rules for MastroNet Inc. December 2003 Auction,”
http://www.mastronet.com/index.cfm?Action=DisplayContent&
ContentName=Rules
McDonald, C.G., Slawson Jr., V.C. (2002), “Reputation in an Internet Auction Market,”
Economic Inquiry, 40:633-651.
Perry, M., Reny, P. (2002), “Notes and Comments an Efficient Auction,” Econometrica,
70:1199-1212.
Roth, A., Ockenfels, A. (2002), “Last-Minute Bidding and the Rules for Ending Second-
Price Auctions: Evidence from eBay and Amazon Auctions on the Internet,” The
American Economic Review, 92:1093-1103.
Major Themes in Economics, Spring 2004
48
Rothkopf, M., Teisberg, T., Kahn, E. (1990), “Why Are Vickrey Auctions Rare?,” The
Journal of Political Economy, 98:94-109.
Steiner, Ina (2002), “Online Auction Sniping: The Thrill of the Hunt,”
AuctionBytes.com,
http://www.auctionbytes.com/cab/abu/y202/m08/abu0077/s02
Swinkels, Jeroen M. (1999), “Asymptotic Efficiency for Discriminatory Private Value
Auctions,” Review of Economic Studies, 66:509-528.
United States Department of Justice (2001), “Plea Agreement of Scott Beach,”
http://www.usdoj.gov/criminal/cybercrime/ebaypleaagree.pdf
Vickrey, William (1961), “Counterspeculation, Auctions, and Competitive Sealed
Tenders,” Journal of Finance, 16:8-37.
